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Abstract

We experimentally demonstrate simultaneous phase and group velocity locking of fundamental and generated second harmonic pulses in Lithium Niobate, under conditions of material phase mismatch. In phase-mismatched, pulsed second harmonic generation in addition to a reflected signal two forward-propagating pulses are also generated at the interface between a linear and a second order nonlinear material: the first pulse results from the solution of the homogeneous wave equation, and propagates at the group velocity expected from material dispersion; the second pulse is the solution of the inhomogeneous wave equation, is phase-locked and trapped by the pump pulse, and follows the pump trajectory. At normal incidence, the normal and phase locked pulses simply trail each other. At oblique incidence, the consequences can be quite dramatic. The homogeneous pulse refracts as predicted by material dispersion and Snell’s law, yielding at least two spatially separate second harmonic spots at the medium’s exit. We thus report the first experimental results showing that, at oblique incidence, fundamental and phase-locked second harmonic pulses travel with the same group velocity and follow the same trajectory. This is direct evidence that, at least up to first order, the effective dispersion of the phase-locked pulse is similar to the dispersion of the pump pulse.

Figures (4)

Numerical simulation of pulsed second-harmonic in a generic Lorentz medium, having γ=10-8, ωp=4, ω0=4, under phase-mismatched conditions. The small γ keeps absorption at negligible levels. The yellow box delineates the medium. (a) pump pulse. (b)SH pulses. Two SH signals are discernable, one that tracks the pumps pulse (yellow arrow), the other that refracts according to material dispersion (red arrow). These two components travel with different group velocities and thus tend to separate as distance is gained inside the sample. The leading pulse is phase-locked and trapped by the pump; the second pulse propagates freely and at a group velocity approximately three times smaller compared to the pump.

The experimental set-up. A prismatic lithium niobate crystal was used to generate the second harmonic 400 nm signal from a 800 nm pump pulse. The titled output face of the crystal forced the pulses to exit at different angles, according to their refractive indices. The locked arm was then refocused onto a thin BBO crystal at perfect phase-matching for ω+2ω=3ω interaction.

Experimental images of the fundamental (800 nm) and second harmonic (400 nm) signals exiting the tilted output surface. Each position corresponds to a different output angle according to the Snell’s law.